Prediction of Heat Transfer in Turbulent Channel Flow With Spanwise Rotation and Suction/Blowing Through Opposite Walls

Abstract

This paper is concerned with the prediction of heat transfer rates in fully-developed turbulent flows in straight channels with mass transfer by suction and blowing through opposite walls, and with rotation about the spanwise axis. The predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using turbulence closures based on the solution of modeled differential transport equations for the Reynolds stresses. A number of alternative models were assessed. These included a high turbulence Reynolds-number model in which the computationally-efficient ‘wall-function’ approach was used to bridge the near-wall region. As the effects of stabilizing system rotation can cause flow relaminarization, the wall-function approach becomes unreliable and integration must be carried out through the viscous sub-layer, directly to the walls. The suitability of three alternative low Reynolds-number models was assessed in these flows. Experimental data from flows in stationary channels with Reynolds numbers spanning the range of laminar, transitional and turbulent regimes were also used in this assessment. Excellent predictions of the wall skin-friction coefficient across the entire range were obtained with a low Reynolds-number model in which the effects of a rigid wall on the fluctuating pressure field in its vicinity were accounted for by a method which incorporates the gradients of the turbulence length scale and the invariants of turbulence anisotropy. For the cases of heated flows, two very different models for the turbulent heat fluxes were examined: one involved the solution of a differential transport equation for each component of the heat-flux tensor and another in which the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. It was found that the two models yielded results that were essentially similar and in close agreement with results from recent Direct Numerical Simulations.